Hello Phil,
Your best solution to the impact noise caused by your neighbor above is to "float" a ceiling on sound clips. You can screw sound clips through your existing ceiling and into the joists about every four square feet. You then put furring channel into the sound clips and attach your drywall to the furring channel. You will leave a gap of a 1/2 inch at the perimeter of your "floated" ceiling. You then fill in the gap with a closed cell foam tape with adhesive on one side called backersquare tape. You then finish this ceiling off by caulking, taping, lightly mudding and then painting. If you wanted extra soundproofing against airborne sounds, you can add a layer of mass loaded vinyl, a one-eighth of an inch thick barrier material.
That being said, there are other factors that can influence the optimal solution to your noise problem. Additional information that could affect your solution would be: Is your ceiling lathe and plaster or drywall? Do you have joists in your ceiling and how far apart are they?
Most likely even with the answers to these questions, your solution will revolve around a "floated" ceiling.
If you would like to discuss your situation further, call 1-888-942-7723
Thank you,
Scott Swisher
Ex- Super Soundproofing Consultant